Polarization-based quantum entanglement for enhanced resolution

Abstract

A quantum LIDAR for improving resolution using quantum entanglement in the polarization degree of freedom is described. A thorough mathematical analysis of this device is provided. A mathematical discussion of how to generate other more robust entangled states is developed. Internal loss within the entanglement generator and external loss due to atmosphere, detectors, and targets are modeled. A method using these approaches for imaging is provided giving N times classical resolution, where N is the number of photons entangled with explicit results exhibited for N = 3. Closed form expressions for the wave function, normalization, density matrix, reduced density matrix, visibility, and probabilities of detection of one through three photons using detectors with general polarization characteristics are provided. An explicit entanglement generator and detector designs are provided in terms of linear and nonlinear photonics devices. The fundamental role of postselection measurement for generating entanglement is included. Discussions of entanglement devices that will produce general M&M states at near-visible frequencies are given. A discussion of a bearing measurement device that exhibits both super sensitivity and resolution is provided. Computational results are provided that compare probabilities of detection for three single photon detectors with −45-deg, 45-deg, and 45-deg linear polarization. Results for detecting one to three photons or the vacuum state are compared. Computational results for detecting three photons with these detectors for various values of internal and atmospheric loss are provided. Resolution improvements born of quantum entanglement are shown not to degrade with loss. Loss degrades probability of detection not resolution.